Estimating downhole fluid volumes using multi-dimensional nuclear magnetic resonance measurements

ABSTRACT

Downhole fluid volumes of a geological formation may be estimated using nuclear magnetic resonance (NMR) measurements, even in organic shale reservoirs. Multi-dimensional NMR measurements, such as two-dimensional NMR measurements and/or, in some cases, one or more well-logging measurements relating to total organic carbon may be used to estimate downhole fluid volumes of hydrocarbons such as bitumen, light hydrocarbon, kerogen, and/or water. Having identified the fluid volumes in this manner or any other suitable manner from the NMR measurements, a reservoir producibility index (RPI) may be generated. The downhole fluid volumes and/or the RPI may be output on a well log to enable an operator to make operational and strategic decisions for well production.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional of U.S. patent application Ser. No. 15/604,029filed May 24, 2017 which claims the benefit of and priority to U.S.Provisional Application No. 62/340,557, titled “Estimating DownholeFluid Volumes Using Two-Dimensional Nuclear Magnetic ResonanceMeasurements” and filed May 24, 2016, which is incorporated by referenceherein in its entirety for all purposes.

BACKGROUND

This disclosure relates to estimating fluid volumes in a geologicalformation using multi-dimensional nuclear magnetic resonance (NMR)measurements.

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the present techniques,which are described and/or claimed below. This discussion is believed tobe helpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentdisclosure. Accordingly, it should be understood that these statementsare to be read in this light, and not as an admission of any kind.

Producing hydrocarbons from a wellbore drilled into a geologicalformation is a remarkably complex endeavor. In many cases, decisionsinvolved in hydrocarbon exploration and production may be informed bymeasurements from downhole well-logging tools that are conveyed deepinto the wellbore. The measurements may be used to infer properties andcharacteristics of the geological formation surrounding the wellbore.

One type of downhole well-logging tool uses nuclear magnetic resonance(NMR) to measure the response of nuclear spins in formation fluids toapplied magnetic fields. Many NMR tools have a permanent magnet thatproduces a static magnetic field at a desired test location (e.g., wherethe fluid is located). The static magnetic field produces an equilibriummagnetization in the fluid that is aligned with a magnetization vectoralong the direction of the static magnetic field. A transmitter antennaproduces a time-dependent radio frequency magnetic field that isperpendicular to the direction of the static field. The radio frequencymagnetic field produces a torque on the magnetization vector that causesit to rotate about the axis of the applied radio frequency magneticfield. The rotation results in the magnetization vector developing acomponent perpendicular to the direction of the static magnetic field.This causes the magnetization vector to align with the componentperpendicular to the direction of the static magnetic field, and toprecess around the static field.

The time for the magnetization vector to re-align with the staticmagnetic field is known as the longitudinal magnetization recovery time,or “T1 relaxation time.” The spins of adjacent atoms precess in tandemsynchronization with one another due to the precession of themagnetization vector. The time for the precession of the spins ofadjacent atoms to break synchronization is known as the transversemagnetization decay time, or “T2 relaxation time.” Thus, themeasurements obtained by downhole NMR tools may include distributions ofthe first relaxation time T1, the second relaxation time T2, ormolecular diffusion, or a combination of these. For example, a downholeNMR tool may measure just T2 distribution, or the tool may measure ajoint T1-T2 distribution or T1-T2-D distribution.

Downhole NMR tools are used to obtain a number of formation evaluationmeasurements. Among other things, downhole NMR tools may be used toevaluate the presence of fluids in the geological formation. Inparticular, the T1 or T2 distributions may be used for estimation offluid volumes. One method for fluid volume estimation appliesuser-specified cutoffs to partition the T2 (or T1) distribution. Thecutoffs are determined empirically from core measurements or are basedon local knowledge. The application of cutoff-based methodology assumesthat the responses of different fluids are independent in the T2 domain.

In many cases, however, the T1 and T2 responses overlap. As such, thecutoff-based methodology may be inaccurate and/or imprecise. Variousmethods have been proposed to overcome this issue. One of those methodsis based on Diffusion-T2 map; however, in the nanometer-size pores ofshale reservoirs, the intrinsic T2 relaxation dominates the relaxationmechanism. As a result, accurately measuring diffusion in thesereservoirs may be difficult or impossible. Another method involves theuse of wet clay porosity (WCLP) and an independent estimate of watersaturation to remove the water signal. Yet this method relies on a veryaccurate value of WCLP, which may involve a core measurement. As such,it may be very difficult to accurately identify fluid volumes using NMRmeasurements in organic shale reservoirs.

SUMMARY

A summary of certain embodiments disclosed herein is set forth below. Itshould be understood that these aspects are presented merely to providethe reader with a brief summary of these certain embodiments and thatthese aspects are not intended to limit the scope of this disclosure.Indeed, this disclosure may encompass a variety of aspects that may notbe set forth below.

Downhole fluid volumes of a geological formation may be estimated usingnuclear magnetic resonance (NMR) measurements, even in organic shalereservoirs. Multi-dimensional NMR measurements, such as two-dimensionalNMR measurements and/or, in some cases, one or more well-loggingmeasurements relating to total organic carbon may be used to estimatedownhole fluid volumes of hydrocarbons such as bitumen, lighthydrocarbon, kerogen, and/or water. Having identified the fluid volumesin this manner or any other suitable manner from the NMR measurements, areservoir producibility index (RPI) may be generated. The downhole fluidvolumes and/or the RPI may be output on a well log to enable an operatorto make operational and strategic decisions for well production.

In one example, a method includes obtaining nuclear magnetic resonancemeasurements and one or more additional log measurements that are atleast collectively sensitive to total organic carbon and using one ormore processors to estimate a fluid volume of a hydrocarbon or a fluidvolume of water, or both. The nuclear magnetic resonance measurementsmay include at least T1 and T2 measurements. The fluid volume of thehydrocarbon, water, or both, may be computed in part by (a) comparingexpected T1-T2 responses for water and hydrocarbon to the nuclearmagnetic resonance measurements to obtain the estimate of the fluidvolume of the hydrocarbon or the estimate of the fluid volume of thewater, or both, (b) computing an uncertainty of the estimate of thefluid volume of the hydrocarbon based at least in part on the one ormore additional log measurements that are at least collectivelysensitive to total organic carbon, (c) computing an uncertainty of theestimate of the fluid volume of the water based at least in part on theone or more additional log measurements that are at least collectivelysensitive to total volume of water, and iteratively performing (a) and(b) or (a) and (c) using one or more variations of the expected T1-T2response for hydrocarbon such that the uncertainty of the estimate isreduced or optimized. One or more tracks of a well log may be generatedusing the estimate of the fluid volume of the hydrocarbon, the estimateof the fluid volume of the water, the uncertainty of the estimate of thefluid volume of the hydrocarbon, or the uncertainty of the estimate ofthe fluid volume of the water, or any combination thereof.

In another example, an article of manufacture may include one or moretangible, non-transitory, machine-readable media that store instructionsthat, when executed by a processor, cause the processor to receive afirst well log measurement comprising a multi-dimensional nuclearmagnetic resonance measurement, receive a second well log measurementthat, alone or in combination with the multi-dimensional nuclearmagnetic resonance measurement, describes a total organic carbonmeasurement of the well, and compute a reservoir producibility index(RPI) based at least in part on the first well log measurement and thesecond well log measurement. The reservoir producibility index (RPI) maybe displayed on a well log.

In another example, a method includes, using a first downhole tooldisposed in a well, obtaining a first well log measurement comprising amulti-dimensional nuclear magnetic resonance measurement using a firstdownhole tool in a well in a geological formation comprising shale and,using the first downhole tool or a second downhole tool disposed in thewell, obtaining a second well log measurement that, alone or incombination with the multi-dimensional nuclear magnetic resonancemeasurement, describes a total organic carbon measurement of the well.Using the first well log measurement and the second well logmeasurement, one or more fluid volumes of hydrocarbon in the well or areservoir producibility index (RPI), or both, may be computed.

Various refinements of the features noted above may be undertaken inrelation to various aspects of the present disclosure. Further featuresmay also be incorporated in these various aspects as well. Theserefinements and additional features may exist individually or in anycombination. For instance, various features discussed below in relationto one or more of the illustrated embodiments may be incorporated intoany of the above-described aspects of the present disclosure alone or inany combination. The brief summary presented above is intended tofamiliarize the reader with certain aspects and contexts of embodimentsof the present disclosure without limitation to the claimed subjectmatter.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of this disclosure may be better understood upon readingthe following detailed description and upon reference to the drawings inwhich:

FIG. 1 is a schematic diagram of a well-logging system that may obtainnuclear magnetic resonance (NMR) logging measurements and/or a loggingmeasurements relating to total organic carbon (TOC) that can be used toestimate fluid volumes, in accordance with an embodiment;

FIG. 2 is a flowchart of a method for using the system of FIG. 1, inaccordance with an embodiment;

FIG. 3 is an example of a map of simulated T1-T2 NMR measurements thatalso illustrates expected T1-T2 responses of various downhole fluids, inaccordance with an embodiment;

FIG. 4 is a flowchart of a method for estimating fluid volumes based atleast in part on a relationship between the expected T1-T2 responses ofthe various downhole fluids and actual NMR measurements, in accordancewith an embodiment;

FIG. 5 is a diagram of a log response matrix showing informationgathered for various types of materials in the geological formation bythe NMR measurements and by other well-logging measurements;

FIG. 6 is a flowchart of a method for refining the expected T1-T2responses of various downhole fluids based on an NMR uncertainty(difference between total organic carbon (TOC) measurements from NMRmeasurements and TOC measurements from other well-logging measurements),in accordance with an embodiment;

FIG. 7 is an example of a map of simulated T1-T2 NMR measurements thatalso illustrates multiple possible expected T1-T2 responses forhydrocarbons, in accordance with an embodiment;

FIG. 8 is a well log representing a visualization of the estimated fluidvolumes of the geological formation and the NMR uncertainty, inaccordance with an embodiment;

FIG. 9 is a flow diagram of a workflow to generate a reservoirproducibility index value using estimated fluid volumes obtained usingNMR data, in accordance with an embodiment;

FIG. 10 is a T1-T2 map of different pore fluids and a table showingcorresponding T1/T2 ratios for the different pore fluids, in accordancewith an embodiment;

FIG. 11 is a T1-T2 map showing an example response for a first shalesample, in accordance with an embodiment;

FIG. 12 is a T1-T2 map showing an example response for a second shalesample, in accordance with an embodiment;

FIG. 13 is diffusion-T2 map showing an example response for a thirdshale sample, in accordance with an embodiment;

FIG. 14 is diffusion-T2 map showing an example response for a fourthshale sample, in accordance with an embodiment; and

FIG. 15 is a well log showing reservoir producibility index generatedusing NMR measurements, in accordance with an embodiment.

DETAILED DESCRIPTION

One or more specific embodiments of the present disclosure will bedescribed below. These described embodiments are examples of thepresently disclosed techniques. Additionally, in an effort to provide aconcise description of these embodiments, certain features of an actualimplementation may not be described in the specification. It should beappreciated that in the development of any such actual implementation,as in any engineering or design project, numerousimplementation-specific decisions may be made to achieve the developers'specific goals, such as compliance with system-related andbusiness-related constraints, which may vary from one implementation toanother. Moreover, it should be appreciated that such a developmenteffort might be complex and time consuming, but would still be a routineundertaking of design, fabrication, and manufacture for those ofordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the presentdisclosure, the articles “a,” “an,” and “the” are intended to mean thatthere are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.Additionally, it should be understood that references to “oneembodiment” or “an embodiment” of the present disclosure are notintended to be interpreted as excluding the existence of additionalembodiments that also incorporate the recited features.

This disclosure describes systems and methods that may be used toestimate downhole fluid volumes of a geological formation using nuclearmagnetic resonance (NMR) measurements, even in organic shale reservoirs.In particular, multi-dimensional NMR measurements, such astwo-dimensional NMR measurements, (and/or, in some cases, one or morewell-logging measurements relating to total organic carbon) may be usedto estimate downhole fluid volumes of bitumen, light hydrocarbon,kerogen, and water. Having identified the fluid volumes in this manneror any other suitable manner from the NMR measurements, a reservoirproducibility index (RPI) may be generated. The RPI may be output on awell log to enable an operator to make operational and strategicdecisions for well production.

With this in mind, FIG. 1 illustrates a well-logging system 10 that mayemploy the systems and methods of this disclosure. The well-loggingsystem 10 may be used to convey a downhole tool 12 through a geologicalformation 14 via a wellbore 16. The downhole tool 12 may be conveyed ona cable 18 via a logging winch system 20. Although the logging winchsystem 20 is schematically shown in FIG. 1 as a mobile logging winchsystem carried by a truck, the logging winch system 20 may besubstantially fixed (e.g., a long-term installation that issubstantially permanent or modular). Any suitable cable 18 for welllogging may be used. The cable 18 may be spooled and unspooled on a drum22 and an auxiliary power source 24 may provide energy to the loggingwinch system 20 and/or the downhole tool 12.

Moreover, although the downhole tool 12 is described as a wirelinedownhole tool, it should be appreciated that any suitable conveyance maybe used. For example, the downhole tool 12 may instead be conveyed as alogging-while-drilling (LWD) tool as part of a bottom hole assembly(BHA) of a drill string, conveyed on a slickline or via coiled tubing,and so forth. For the purposes of this disclosure, the downhole tool 12may be any suitable measurement tool that obtains NMR loggingmeasurements through depths of the wellbore 16 and/or obtains a non-NMRmeasurement of total organic carbon (TOC). Indeed, it should beappreciated that these different measurements (NMR and a non-NMRmeasurement of TOC) may be obtained even by different logging toolsand/or logging systems. For example, TOC measurements may be obtained ina first well-logging operation, and the NMR measurements may be obtainedin a second well-logging operation, and so forth.

Many types of downhole tools may obtain NMR logging measurements in thewellbore 16. These include, for example, nuclear magnetic resonance(NMR) tools such as the Combinable Magnetic Resonance (CMR) tool, theMagnetic Resonance Scanner (MRX) tool, and the ProVISION tool bySchlumberger Technology Corporation. In general, NMR tools may have apermanent magnet that produces a static magnetic field at a desired testlocation (e.g., where the fluid is located). The static magnetic fieldproduces an equilibrium magnetization in the fluid that is aligned witha magnetization vector along the direction of the static magnetic field.A transmitter antenna produces a time-dependent radio frequency magneticfield that is perpendicular to the direction of the static field. Theradio frequency magnetic field produces a torque on the magnetizationvector that causes it to rotate about the axis of the applied radiofrequency magnetic field. The rotation results in the magnetizationvector developing a component perpendicular to the direction of thestatic magnetic field. This causes the magnetization vector to alignwith the component perpendicular to the direction of the static magneticfield, and to precess around the static field.

The time for the magnetization vector to re-align with the staticmagnetic field is known as the longitudinal magnetization recovery time,or “T1 relaxation time.” The spins of adjacent atoms precess in tandemsynchronization with one another due to the precession of themagnetization vector. The time for the precession of the spins ofadjacent atoms to break synchronization is known as the transversemagnetization decay time, or “T2 relaxation time.” Thus, themeasurements obtained by the downhole tool 12 may include distributionsof the first relaxation time T1, the second relaxation time T2, ormolecular diffusion D, or a combination of these. For example, adownhole NMR tool may measure just T2 distribution, or the tool maymeasure a joint T1-T2 distribution or T1-T2-D distribution.

For each depth of the wellbore 16 that is measured, a downhole NMR toolmay generate NMR logging measurements that include a distribution ofamplitudes of T2 relaxation time, T1 relaxation time, diffusion, or acombination thereof. This list is intended to present certain examplesand is not intended to be exhaustive. Indeed, any suitable downhole tool12 that obtains NMR logging measurements may benefit from the systemsand methods of this disclosure.

The downhole tool 12 may provide logging measurements 26 to a dataprocessing system 28 via any suitable telemetry (e.g., via electricalsignals pulsed through the geological formation 14 or via mud pulsetelemetry). The data processing system 28 may process the NMR loggingmeasurements 26 to identify patterns in the NMR logging measurements 26.The patterns in the NMR logging measurements 26 may indicate certainproperties of the wellbore 16 (e.g., viscosity, porosity, permeability,relative proportions of water and hydrocarbons, and so forth) that mightotherwise be indiscernible by a human operator. A total organic carbon(TOC) measurement may be used to further refine the manner in which thepatterns in the NMR logging measurements are used to identify downholefluid volumes.

To this end, the data processing system 28 thus may be any electronicdata processing system that can be used to carry out the systems andmethods of this disclosure. For example, the data processing system 28may include a processor 30, which may execute instructions stored inmemory 32 and/or storage 34. As such, the memory 32 and/or the storage34 of the data processing system 28 may be any suitable article ofmanufacture that can store the instructions. The memory 32 and/or thestorage 34 may be ROM memory, random-access memory (RAM), flash memory,an optical storage medium, or a hard disk drive, to name a few examples.A display 36, which may be any suitable electronic display, may providea visualization, a well log, or other indication of properties (e.g.,downhole fluid volumes) in the geological formation 14 or the wellbore16 based on the NMR logging measurements 26.

Here, it may be noted that modern NMR tools may be capable of acquiringT1 and T2 measurements either as continuous depth logs or stationarymeasurements. In several cases, there is a contrast in the T1-T2response of fluids. For example, the T1/T2 ratio of high viscosityfluids such as bitumen can be an order of magnitude higher compared tothat for other formation fluids. Similarly, in organic shale reservoirs,core measurements show that the T1/T2 ratio of oil is greater than thatfor water. Therefore, T1-T2 measurements may be used for the estimationof fluid volumes. However, there are two challenges in estimation offluid volumes from T1-T2 measurements. First, the NMR measurements mayhave a relatively poor signal-to-noise ratio (SNR), which could resultin an inadequate resolution of features on T1-T2 distributions. Second,the T1-T2 response of formation fluids may be highly variable. Acalibration with core measurements may be used to obtain accurateestimation of fluid volumes. To overcome these concerns, the fluidvolumes determined based on T1-T2 distributions may be refined based onone or more non-NMR measurements of total organic carbon (TOC), therebyreducing uncertainty of the estimates of fluid volume. Additionally oralternatively, other NMR measurements, such as diffusion, may beobtained.

A flowchart 50 of FIG. 2 describes one way to accurately estimatedownhole fluid volumes from NMR measurements, even in shale reservoirs.Namely, the downhole tool 12 may be placed in the wellbore 16 (block 52)and an NMR measurement (e.g., T1 and T2 measurement) of the wellbore 16may be obtained (block 54). The same downhole tool 12 or a differentdownhole tool may obtain one or more measurements at least collectivelysensitive to total organic carbon (TOC) or total water (block 56). Thatis, while the same downhole tool 12 may be used to obtain both the NMRmeasurements and the TOC or total water measurement(s), this does nothave to be the case. Indeed, these measurements may be obtained atdifferent times and/or with different downhole tools, including bydifferent downhole tools of different conveyances. In one non-limitingexample, the TOC or total water measurement(s) may be obtained in alogging while drilling (LWD) tool when the wellbore is first drilled,and the NMR measurement may be obtained subsequently using a wireline(WL) tool.

The data processing system 28 may use the NMR measurement (and, in atleast some cases, the TOC measurement) to estimate likely values offluid volumes of bitumen, light hydrocarbons, kerogen, and/or water evenin shale reservoirs. For example, the data processing system 28 maycompare expected T1-T2 responses for water and for hydrocarbons to theactual NMR measurements to estimate fluid volume fractions (block 56).It may be noted that while the expected T1-T2 response for water may befairly consistent, the expected T1-T2 response for hydrocarbons mayvary. As such, the data processing system 28 may use non-NMR TOCmeasurements to determine an uncertainty of the identified fluidvolumes, as well as to refine the accuracy of the expected T1-T2response for hydrocarbons by reducing the uncertainty (block 60). Thus,it may be appreciated that blocks 58 and 60 may be performed iterativelyto achieve a desired (e.g., reduced or optimized) level of uncertainty.The likely fluid volumes and/or a reservoir producibility index based atleast in part on the fluid volumes and TOC measurement may be outputonto a well log (block 62), which may enable decisionmakers to makeproduction and recovery decisions tailored to the conditions of thegeological formation 14.

Estimating Fluid Volumes from T1-T2 NMR Measurements

As noted above, in several cases, there is a contrast in the T1-T2response of fluids. This is shown by example in FIG. 3, which shows aT1-T2 map 70 of synthetic (simulated) NMR measurements from a geologicalformation 14 that contains water, bitumen, and light hydrocarbons. TheT1-T2 map 70 illustrates synthetic NMR measurements of T1 relaxationtime (ordinate 72) and T2 relaxation time (abscissa 74) each on alogarithmic scale. A first curve 76 represents a likely T1-T2 responseof hydrocarbons, while a second curve 78 represents a likely T1-T2response of water. A third curve 80 represents a logarithmic mean of themeasured values of the T1 distribution at each T2. Based on therelationship between the third curve 80 to the first curve 76 and thesecond curve 78, estimated fluid volumes may be identified. Although thefirst curve 76 and the second curve 78 are shown in FIG. 3 to have fixedratios, the first curve 76 may take any suitable functional form.Indeed, the T1-T2 response for either fluid may have a fixed or variableratio. FIG. 3 shows a case in which the T1-T2 response of water isrepresented to have a fixed T1-T2 ratio (curve 78) whereas the T1-T2response of hydrocarbon is represented to have a higher T1/T2 ratio atthe shorter end of T2 and lower T1/T2 ratio at the longer end (curve76). This is based on laboratory measurements, which have shown thatT1/T2 ratio values for bitumen may be higher compared to low viscosityoil. Moreover, as discussed below, the T1-T2 response for hydrocarbonmay be a static, predetermined ratio or may be dynamically adjustedbased on one more other log measurements that is at least collectivelysensitive to total organic carbon (TOC).

Bitumen and light hydrocarbon have distinct T2 responses. As such, theT1-T2 map 70 of FIG. 3 may be partitioned using a cutoff value of T2,illustrated in FIG. 3 as T_(2,b), that may define whether a hydrocarbonis likely bitumen or a light hydrocarbon. Namely, values of the T1-T2distribution beneath T_(2,b) may be more likely due to bitumen 82, whilevalues of the T1-T2 distribution above T_(2,b) may be more likely due tolight hydrocarbons 84. The particular value of T_(2,b) that separatesbitumen from light hydrocarbons may be determined in any suitable way(e.g., through empirical laboratory measurements orcomputer-simulations).

Based on the expected T1-T2 responses, such as those illustrated ascurves 76 and 78 in the T1-T2 map 70 of FIG. 3, downhole fluid volumesfor water, bitumen, and light hydrocarbons may be estimated. Oneparticular example appears in a flowchart 90 of FIG. 4. The flowchart 90begins when NMR measurements including T1 and T2 distributions arereceived into the data processing circuitry 28 (block 92). These may bereceived in real time or near real time from the downhole tool 12, ormay be retrieved from any suitable electronic storage after the downholetool 12 has completed logging the wellbore 16.

In practice, although fluid amplitudes may be broadened and indistincton the T1-T2 map due to relatively poor SNR and regularization, the meanof the total distribution corresponds to the volumetric average offluids that make up the NMR signal. Thus, for each T2, an average T1 canbe computed as the logarithmic mean of the T1 distribution (T1LM) (block94). This is represented in FIG. 3 as the curve 80, and may becalculated using the following expression:

$\begin{matrix}{{F\left( T_{2_{i}} \right)} = {\sum\limits_{j}{F\left( {{T\; 2_{i}},{T\; 1_{j}}} \right)}}} & (1) \\{{T\; 1\;{LM}_{i}} = 10^{\frac{\sum\limits_{1}^{{nt}\; 1}{{logT}\; 1_{j}*\phi_{i,j}}}{F{({T\; 2_{i}})}}}} & (2)\end{matrix}$where i and j represent the indices along the T2 and T1 dimensions,respectively, of the T1-T2 map 70.

To identify bitumen, light hydrocarbon, and water saturation, thehydrocarbon and water signals then can be redistributed according to thedeparture of the T1 of each fluid from the T1LM line (curve 80) (block96). The saturation of the two hydrocarbon constituents can be estimatedas a function of 72:

$\begin{matrix}{{{S_{BIT}\left( {T\; 2_{i}} \right)} = {{\frac{\ln\left( \frac{T\; 1_{LM}\left( {T\; 2_{i}} \right)}{T\; 1{W\left( {T\; 2_{i}} \right)}} \right)}{\ln\left( \frac{T\; 1\;{O\left( {T\; 2_{i}} \right)}}{T\; 1{W\left( {T\; 2_{i}} \right)}} \right)}i} = 1}},\;{.\;.\;.}\mspace{14mu},b} & (3) \\{{{S_{LHC}\left( {T\; 2_{i}} \right)} = {{\frac{\ln\left( \frac{T\; 1_{LM}\left( {T\; 2_{i}} \right)}{T\; 1{W\left( {T\; 2_{i}} \right)}} \right)}{\ln\left( \frac{T\; 1\;{O\left( {T\; 2_{i}} \right)}}{T\; 1{W\left( {T\; 2_{i}} \right)}} \right)}i} = {b + 1}}},\;{.\;.\;.}\mspace{14mu},n} & (4)\end{matrix}$

In the above equation, T1 W and T1O refer to the T1 values of water andhydrocarbon respectively computed from the T1-T2 response lines (curves78 and 76, respectively). The index b represents the T2 cutoff used topartition the map into bitumen and light hydrocarbon regions. If theT1LM is greater than the T1O, the amplitude is attributed tohydrocarbon. Similarly, if the T1LM lies below T1W, the amplitude isattributed to water.

The volume fractions of bitumen (Ø_(BIT)), light hydrocarbon (Ø_(LHC)),and water (Ø_(W)) can be calculated based on the fluid saturation values(block 98). For example, these volume fractions may be given as:Ø_(BIT) =ΣS _(BIT)(T2_(i))*F(T2_(i))  (5)Ø_(LHC) =ΣS _(LHC)(T2_(i))*F(T2_(i))  (6)Ø_(W) =ΣF(T2_(i))−Ø_(BIT)−Ø_(LHC)  (7)

The fluid saturations and/or the volume fractions of bitumen, lighthydrocarbon, and/or water may be output to any suitable electronicstorage or to a well log (block 100). However, the main uncertainty inthe method is due to the unknown value of T1-T2 response of hydrocarbon,which can vary substantially. This issue can be addressed by integratingthe T1-T2 measurement with one or more log measurements sensitive to thetotal oil or water volume. Thus, additionally or alternatively, theexpected T1-T2 responses of hydrocarbons may be iteratively adjusted toreduce the uncertainty of the fluid saturations and/or the volumefractions based on the one or more log measurements sensitive to thetotal oil or water volume.

Estimating Uncertainty of Fluid Volumes and/or Refining Expected T1-T2Responses

While it is possible to estimate fluid volumes from NMR measurementsbased on a predetermined expected T1-T2 response to hydrocarbon, adynamic expected T1-T2 response may be more accurate. Thus, the methodmay be enhanced by estimating a degree of uncertainty of the fluidvolumes and/or further refining the expected T1-T2 response based on oneor more log measurements that are at least collectively sensitive to thetotal organic carbon (TOC) of the geological formation.

Total organic carbon (TOC) is the amount of the organic carbon thatresides within the geological formation and is measured as dry weightpercent of carbon per unit mass of matrix components. In geologicalformations where the only source of organic carbon is oil, the TOC canbe converted into the volume fraction of oil (ϕ_(OIL)) by relating itwith the carbon content in a unit mass of oil and expressing in terms ofthe component volumes and densities as:

$\begin{matrix}{{TOC} = \frac{\phi_{OIL} \cdot \rho_{OIL} \cdot X_{C}}{\rho_{m}\left( {1 - \phi_{T}} \right)}} & (8)\end{matrix}$where X_(C) and ρ_(OIL) represent the carbon weight fraction and densityof oil, respectively; ρ_(m) represents the matrix density; and Ø_(T)represents total porosity. In formations containing kerogen, bitumen,and light hydrocarbon, the TOC is the sum of the carbon concentrationfrom those three components. Bulk density, matrix density, TOC and T1-T2measurements may be used to quantify the volumes of kerogen, bitumen,and light hydrocarbon.

FIG. 5 illustrates a log response matrix 110 illustrating responses ofvarious components of a geological formation (e.g., an organic shalereservoir) to different types of logging measurements. The variouscomponents shown in FIG. 5 include inorganic dry rock 112, kerogen 114,bitumen 116, clay-bound water 118, light hydrocarbon 120, and intra-porewater 122. As can be seen, NMR logging measurements 124 are sensitive tomost bitumen 116, clay-bound water 118, light hydrocarbon 120, andintra-pore water 122. By contrast, a total organic carbon (TOC) loggingmeasurement may be sensitive to the hydrocarbon components of thegeological formation, which include kerogen 114, bitumen 116, and lighthydrocarbon 120. A matrix density logging measurement 128 is sensitiveto inorganic dry rock, and bulk density 130 is sensitive to each of thecomponents of FIG. 5.

As shown by a flowchart 140 of FIG. 6, an uncertainty of the fluidvolumes may be estimated using any suitable logging measurements, suchas the logging measurements shown in FIG. 5. From this uncertainty, theexpected T1-T2 response to hydrocarbon may be further refined. In theflowchart 140, the one or more logging measurements that are at leastcollectively sensitive to total organic carbon (TOC) may be received bythe data processing circuitry 28. While the example of FIG. 6 discussesuncertainty in relation to total organic carbon (TOC), it should beappreciated that uncertainty in relation total volume of water may alsobe used to determine uncertainty for water volume using well logs thatare at least collectively sensitive to total volume of water compared towater volume computed via NMR measurements. In the example of FIG. 6,the one or more logging measurements include bulk density, matrixdensity, TOC, and T1-2 measurements. In a shale oil reservoir, the bulkdensity (ρ_(B)) is the volumetric average of matrix density (ρ_(m)),kerogen density (Ø_(K)), and pore fluid density (ρ_(Fl)), and can bespecified in relation to total porosity (Ø_(T)) as:ρ_(B)=ρ_(m)(1−Ø_(T)−Ø_(K))+ρ_(K)Ø_(K)+ρ_(Fl)Ø_(T)  (9)

Because kerogen is solid and does not constitute any NMR signal, the NMRmeasurement provides a direct estimate of total porosity. This isespecially true for NMR tools with short inter-echo time, where the lossof signal due to bitumen is small. As such, total porosity may bereplaced with NMR porosity (MRP) in Equation 9 to estimate the volume ofkerogen (block 144). The volume of kerogen (ϕ_(K)) can be estimated as:

$\begin{matrix}{\phi_{K} = {\frac{\rho_{m} - \rho_{B}}{\rho_{m} - \rho_{K}} - {({MRP})*\frac{\rho_{m} - \rho_{fl}}{\rho_{m} - \rho_{K}}}}} & (10)\end{matrix}$

Using Equation 8 for volume of kerogen, the amount of carbon due tokerogen can be subtracted from TOC to estimate the sum of carbon due tobitumen and light hydrocarbon (TOC_(OIL)) (block 146). This may becomputed, for example, as:

$\begin{matrix}{{TOC}_{OIL} = {{TOC} - \frac{\phi_{K} \cdot \rho_{K} \cdot X_{K}}{\rho_{m} \cdot \left( {1 - \phi_{T} - \phi_{k}} \right)}}} & (11)\end{matrix}$where X_(K) represents kerogen weight fraction.

The volumes of bitumen and light hydrocarbon estimated from theT1LM-based interpretation of T1-T2 map can be used to estimate anapparent TOC from NMR (block 148). For example, this may be computed as:

$\begin{matrix}{{TOC}_{{NMR},{app}} = \frac{X_{C}\left( {{\phi_{LHC} \cdot \rho_{LHC}} + {\phi_{BIT} \cdot \rho_{BIT}}} \right)}{\rho_{m} \cdot \left( {1 - \phi_{T} - \phi_{k}} \right)}} & (12)\end{matrix}$where ρ_(BIT) represents a density of the bitumen and ρ_(LHC) representsa density of the light hydrocarbon.

The biggest uncertainty in interpreting T1-T2 map is due to the unknownT1-T2 response of hydrocarbon. It is expected that the TOC_(NMR, app)matches with the TOC_(OIL). Hence, the T1-T2 response of hydrocarbon canbe estimated iteratively such that a difference between theTOC_(NMR, app) and TOC_(OIL) is reduced to a desired difference orminimized (block 150). The difference may be represented as anuncertainty (TOC_(SIG)) as follows:|TOC_(OIL)−TOC_(NMR),app|≈TOC_(SIG)  (13)

The TOC_(SIG) is the TOC uncertainty. The method is self-consistent inthat the estimated total hydrocarbon volume is equivalent of themeasured TOC within its uncertainty value. The fluid saturations and/orthe volume fractions of kerogen, bitumen, light hydrocarbon, and/orwater may be output to a well log (block 152). If desired, the totalorganic carbon (TOC) and the uncertainty (TOC_(SIG)) may be outputalongside these values. An example of this is shown in FIG. 8, whichwill be discussed further below.

Indeed, before continuing further, FIG. 7 illustrates an example ofdynamic adjustments to the expected T1-T2 response of hydrocarbon thatmay be made in the iterative approach discussed with reference to block150. FIG. 7 once again illustrates the T1-T2 map 70 of synthetic(simulated) NMR measurements from a geological formation 14 thatcontains water, bitumen, and light hydrocarbons. It may be recalled thatthe T1-T2 map 70 illustrates synthetic NMR measurements of T1 relaxationtime (ordinate 72) and T2 relaxation time (abscissa 74), each on alogarithmic scale. The curve 78 represents a likely T1-T2 response ofwater and the curve 80 represents a logarithmic mean of the measuredvalues of the T1 distribution at each T2. The curves 76A, 76B, and 76Cthat appear in FIG. 7 illustrate possible variations of the T2-T2response of hydrocarbon. In other words, the curves 76A, 76B, and 76C ofFIG. 7 may represent dynamic adjustments of the curve 76 shown in FIG.3. Each of the curves 76A, 76B, and 76C shown in FIG. 7 has a differentT1/T2 ratio that may describe the T1-T2 response of hydrocarbon moreaccurately or less accurately than others. Indeed, a circled number 155on the T1-T2 map 70 represents a T1/T2 ratio value for hydrocarbon inlarge pores (here, a value of 2). Circled numbers 156, 157, and 158represent possible T1/T2 ratio values for bitumen (here, 20, 10, and 3,respectively), which results in large variation in expected T1-T2response relating to oil saturation.

FIG. 8 is an example of a well log 160 that may provide a visualizationof the properties estimated in accordance with the systems and methodsdiscussed above. The well log 160 includes four tracks: 162, 164, 166,and 168. The first track 164 represents well depth in units of feet. Thesecond track 162 includes total organic carbon (TOC) 170 and ameasurement of its uncertainty (TOC_(SIG)) 172. The third track 164includes density porosity 174 alongside NMR porosity (MRP) 176. Thefourth track 166 includes a volume fraction of light hydrocarbon 178, avolume fraction of bitumen 180, a volume fraction of kerogen 182, and avolume fraction of water 184. By presenting the identified underlyingfeatures in a visualization such as this, a human operator may be ableto effectively make decisions relating to the management and/oroperation of the well.

Workflow to Generate Reservoir Producibility Partly Using NMRMeasurements

As noted above, total organic carbon (TOC) in unconventional tight oilplays can be divided into multiple fractions: mobile oil (lighthydrocarbon), bitumen (immobile and soluble in organic solvent), andkerogen (immobile and insoluble in organic solvent). Whereas abundantmobile oil is a positive reservoir quality (RQ) indicator, abundantkerogen and bitumen have been shown to reduce permeability by swellingand by clogging pore throats, respectively, and therefore can benegative reservoir quality indicators. Multi-dimensional NMRmeasurements may be used to determine a reservoir producibility index(RPI) downhole, potentially avoiding a reliance on cuttings or cores,which can be unrepresentative of the formation because mobile fluidsescape from cuttings in the borehole or during the analysis. Moreover,an RPI determined using NMR measurements may be used even in locationsthat contain substantial quantities of bitumen or kerogen. Indeed, NMRmeasurements may provide the understanding the fluid types andvolumetrics of these fractions in tight oil reservoirs, which couldgreatly assist with production. In summary, a workflow involvingseparate consideration of oil, bitumen, and kerogen may provide moreinsight than workflows that simply group these quantities together asTOC, because oil is a positive reservoir quality indicator, whereaskerogen and bitumen can be negative reservoir quality indicators.

Reservoir Producibility Index (RPI) can be expressed as:

$\begin{matrix}{{RPI} = {W_{C\_ Oil} \times \frac{W_{C\_ Oil}}{TOC}}} & (14)\end{matrix}$where W_(C_Oil) is the carbon weight fraction of light oil and can becalculated using the light oil porosity obtained from 2D NMR T1-T2and/or D-T2 logs as discussed herein or using other techniques. Forexample, the carbon weight fraction of light oil W_(C_Oil) may becalculated as follows:

$\begin{matrix}{W_{C\_ Oil} = \frac{k \times \phi_{oil} \times \rho_{oil}}{\rho_{b}}} & (15)\end{matrix}$

In Equation 15 above, the factor k is the ratio between carbon weight oflight oil and total light oil weight, Φ_(oil) and the ρ_(oil) are theoil porosity and density, and ρ_(b) is the bulk density of theformation.

As mentioned above, TOC is total organic carbon of the formation, whichcan be measured from the downhole spectroscopy log or calculated usingthe carbon weight fraction of log-derived kerogen, plus boundhydrocarbon and/or bitumen and light oil from 2D NMR T₁-T₂ and/or D-T2logs, respectively:TOC=W _(C_Oil) +W _(C_Bitumen) +W _(C_Kerogen)  (16)

One example is a workflow 200 shown in FIG. 9. The workflow 200 may beused to generate a well log of reservoir producibility index (RPI) 202using a workflow that uses certain fluid volume fractions obtained frommulti-dimensional NMR measurements. Spectroscopy measurements 204 orother well logs (e.g., such as the “triple combo” of density, porosity,and resistivity) may be obtained using any suitable spectroscopy tool orother downhole tool, from which formation mineralogy and TOC 206 can beestimated. In many cases, formation mineralogy and TOC 206 can bedirectly obtained from the spectroscopy log 204. If the spectroscopy logis not available, the mineralogy may be characterized using other logsthrough formation evaluation 210, and TOC may be estimated using othercorrelation methods (e.g., Schmoker, Δ log R, or Uranium quantities).Oil-filled porosity Ø_(Oil) and water-filled porosity Ø_(W) can bequantified using the 2D NMR T₁-T₂ and/or D-T₂ logs in the mannerdiscussed above or using any other suitable technique. The reservoirproducibility index (RPI) 202 can be calculated using Equations 14-16.

Different materials may appear in different locations on amultidimensional NMR map, such as a T1-T2 map. FIG. 10 shows a varietyof different types of materials that could be classified based on theirlocation in a T1-T2 map 220. The T1-T2 map 220 illustrates synthetic NMRmeasurements of T1 relaxation time (ordinate 72) and T2 relaxation time(abscissa 74) each on a logarithmic scale. The T1-T2 map 220 includeslines that represent different T1/T2 ratios across the T1-T2 map 220. Inparticular, the T1-T2 map 220 shown in FIG. 10 includes a line 222illustrating a T1/T2 ratio of 1, a line 224 illustrating a T1/T2 ratioof 2, a line 226 illustrating a T1/T2 ratio of 5, and a line 228illustrating a T1/T2 ratio of 10. The appearance of NMR measurementsalong different T1/T2 ratios, and thus across the lines 222, 224, 226,and 228, may be one way to identify the type of pore fluid that has beendetected in the NMR measurements. In addition, certain pore fluids maybe visible in low field NMR (at values of T2 higher than a threshold230, which may be, in some examples, signals greater than about 2 MHz).

The different pore fluids located on the T1-T2 map 220 include kerogen232, bitumen 234, clay-bound water 236, immovable oil in organicporosity (OP) 238, movable oil in organic porosity (OP) 239, oil ininorganic porosity (IP) 240, water in inorganic porosity (IP) 242, oil244, water 246, and gas 248. The corresponding T1/T2 ratio is shown in atable 250. The T1/T2 ratios of bulk fluids or fluids in large pores areclose to 1. As pore sizes become smaller, T2 becomes shorter and T1/T2ratio becomes higher. The T1/T2 ratio of hydrocarbon is higher than thatof water. Therefore, for tight oil reservoirs, water and oil signals canpotentially be separated with proper T2 and T1/T2 ratio basedidentifications. These may be done in the manner discussed above orusing any other suitable techniques.

FIG. 11 is an example of a T1-T2 map 270 that identifies pore fluids ina first shale sample. The T1-T2 map 270 illustrates NMR measurements ofT1 relaxation time (ordinate 72) and T2 relaxation time (abscissa 74)each on a logarithmic scale. The T1-T2 map 270 includes lines thatrepresent different T1/T2 ratios across the T1-T2 map 270. Inparticular, the T1-T2 map 270 shown in FIG. 11 includes a line 272illustrating a T1/T2 ratio of 1, a line 274 illustrating a T1/T2 ratioof 1.59, a line 276 illustrating a T1/T2 ratio of 3.59, and a line 278illustrating a T1/T2 ratio of 11.5, each of which passes through a localpeak of the NMR measurements on the T1-T2 map 270. By comparing thelocation of the peaks of the measured T1 and T2 NMR measurements to thepreviously identified locations of various pore fluids (e.g., asillustrated in FIG. 10), the T1-T2 map 270 can be shown to haveidentified bitumen and bound water in a region 280, oil in organic poresin a region 282, and oil in inorganic pores in a region 284.

FIG. 12 is an example of a T1-T2 map 290 that identifies pore fluids ina second shale sample. The T1-T2 map 290 illustrates NMR measurements ofT1 relaxation time (ordinate 72) and T2 relaxation time (abscissa 74)each on a logarithmic scale. The T1-T2 map 290 includes lines thatrepresent different T1/T2 ratios across the T1-T2 map 290. Inparticular, the T1-T2 map 290 shown in FIG. 12 includes a line 292illustrating a T1/T2 ratio of 1, a line 294 illustrating a T1/T2 ratioof 1.79, and a line 296 illustrating a T1/T2 ratio of 6.42, each ofwhich passes through a local peak of the NMR measurements on the T1-T2map 290. By comparing the location of the peaks of the measured T1 andT2 NMR measurements to the previously identified locations of variouspore fluids (e.g., as illustrated in FIG. 10), the T1-T2 map 290 can beshown to have identified bitumen and bound water in a region 298, oil inorganic pores in a region 300 (which may be more likely to be immovableoil in comparison to the oil of region 282 of FIG. 11), and oil ininorganic pores in a region 304. It may be noted that, additionally oralternatively, the oil and water signatures and volumes may beidentified using model-independent, data-mining based approaches.

At longer relaxation times, the oil and water in the inorganic poresmight have similar T1 and T2 behaviors. This implies that a measurementother than T1-T2 2D maps might more effectively separate these twofractions. In such cases, NMR diffusion measurements may be used toidentify the fluids based on the differences in the diffusioncoefficients between the aqueous and hydrocarbon fractions. Examples of2D diffusion-T2 maps appear in FIGS. 13 and 14. In FIG. 13, a D-T2 map310 illustrates NMR measurements of molecular diffusion (ordinate 312)and T2 relaxation time (abscissa 74) each on a logarithmic scale for athird shale sample. Here, the oil in the inorganic pores can beidentified (portions of the signal located below an aqueous threshold314) in comparison to fluids that are more likely water (portions of thesignal located above the aqueous threshold 314). In FIG. 14, anotherD-T2 map 330 illustrates NMR measurements of molecular diffusion(ordinate 312) and T2 relaxation time (abscissa 74) each on alogarithmic scale in a fourth shale sample. Here, the oil in theinorganic pores can be identified (portions of the signal located belowan aqueous threshold 314) in comparison to fluids that are more likelywater (portions of the signal located above the aqueous threshold 314).

The workflow 200 described with reference to FIG. 9 may be used toproduce a reservoir producibility index (RPI) 202 that may effectivelyidentify the reservoir quality in a well log. FIG. 15 provides anexample well log 350 that may include a number of tracks including anRPI value determined as provided in this disclosure. The well log 350includes several tracks 352, 354, 356, 358, 360, 362, 364, 366, 368,370, and 372. These tracks are intended to represent the type ofinformation that may appear in a well log, and these tracks are notmeant to be exhaustive. Indeed, more or fewer tracks may be present inany actual well log that is developed in accordance with the workflow ofthis disclosure. Returning to the example well log 350 of FIG. 15, thetracks may present the following information:

Track 352: depth track.

Track 354: T₂ distribution from 2D NMR T₁-T₂ log with T₂LM and T₂ cutoffof 3.0 ms to separate bound and effective porosities.

Track 356: T₁ distribution from 2D NMR T₁-T₂ log with T₁LM.

Track 358: Porosity from 2D NMR log in comparison to the porosity fromcore data.

Track 360: Volumetric results of mineralogy and fluids from formationevaluation using spectroscopy and 2D NMR logs.

Track 362: Fluid porosity logs from 2D NMR T₁-T₂ log using the cutoffsdisplayed in FIG. 3.

Track 364: Clay-bound water porosity from 2D NMR log in comparison tothat from core data.

Track 366: Bound hydrocarbon porosity from 2D NMR log in comparison tothat from core data.

Track 368: Effective porosity from 2D NMR log using T₂ cutoff of 3.0 msin comparison to that from core data.

Track 370: Effective water porosity from 2D NMR log in comparison to theeffective water porosity calculated from resistivity.

Track 372: Calculated RPI 202 (line) from the workflow 200 in comparisonto a carbon weight fraction 374 (dots) of producible hydrocarboncalculated from the core data.

Indeed, as may be seen in track 372, the RPI 202 calculated using themulti-dimensional NMR measurements is very well correlated to thecore-sample-based measure of carbon weight fraction 374. This suggeststhat the RPI 202 may serve as a highly valuable addition or alternativeto a core sample, since the RPI 202 can be calculated using downholemeasurements that might more accurately capture the state of thedownhole fluids in the downhole environment. Having generated and outputthe RPI 202 onto a well log such as the well log 350, an operator orother decisionmaker may more effectively make production and recoverydecisions tailored to the conditions of the geological formation 14.

The specific embodiments described above have been shown by way ofexample, and it should be understood that these embodiments may besusceptible to various modifications and alternative forms. It should befurther understood that the claims are not intended to be limited to theparticular forms disclosed, but rather to cover modifications,equivalents, and alternatives falling within the spirit and scope ofthis disclosure.

The invention claimed is:
 1. An article of manufacture comprising one or more tangible, non-transitory, machine-readable media comprising instructions that, when executed by a processor, cause the processor to: receive a first well log measurement comprising a multi-dimensional nuclear magnetic resonance measurement obtained by a first downhole tool in a well; receive a second well log measurement that, alone or in combination with the multi-dimensional nuclear magnetic resonance measurement, describes a total organic carbon measurement of the well, wherein the second well log measurement is obtained by the first downhole tool or a second downhole tool in the well; compute a reservoir producibility index (RPI) based at least in part on the first well log measurement and the second well log measurement, wherein the instructions to compute the reservoir producibility index (RPI) comprise instructions to: compute a carbon weight fraction of light oil W_(C_Oil) on based at least in part on the first well log measurement; compute a total organic carbon (TOC) based at least in part on the second well log measurement; and compute the reservoir producibility index (RPI) using the carbon weight fraction of light oil W_(C_Oil) and the total organic carbon (TOC); and wherein the instructions to compute the carbon weight fraction of light oil W_(C_Oil) comprise instructions to: (a) compare expected multi-dimensional nuclear magnetic resonance responses for water and hydrocarbon to the actual multi-dimensional nuclear magnetic resonance responses from the first well log measurement to obtain an estimate of one or more fluid volumes of the hydrocarbon, wherein the one or more fluid volumes of the hydrocarbon comprises the carbon weight fraction of light oil W_(C_Oil) or a value that can be used to obtain the carbon weight fraction of light oil W_(C_Oil); (b) compute an uncertainty of the estimate of the fluid volume of the hydrocarbon based at least in part on the second well log measure; and iteratively perform (a) and (b) using one or more variations of the expected multi-dimensional nuclear magnetic resonance responses for water and hydrocarbon to cause the uncertainty of the estimate to be reduced or optimized; and display the reservoir producibility index (RPI) on a well log.
 2. The article of manufacture of claim 1, wherein the first well log measurement comprises a 2D nuclear magnetic resonance measurement of T1 and T2.
 3. The article of manufacture of claim 1, wherein the first well log measurement comprises a 2D nuclear magnetic resonance measurement of diffusion (D) and T2.
 4. The article of manufacture of claim 1, wherein the second well log measurement comprises a spectroscopy measurement.
 5. The article of manufacture of claim 1, wherein the second well log measurement comprises one or more well log values from which total organic carbon (TOC) may be obtained.
 6. The article of manufacture of claim 1, wherein: the carbon weight fraction of light oil W_(c_oil) is computed in accordance with the following relationship: W _(C_Oil)=(k×φ _(oil)×ρ_(oil))/ρ_(b) where k is the ratio between carbon weight of light oil and total light oil weight, ϕ_(oil) and the ρ_(oil) are the oil porosity and density, and ρ_(b) is the bulk density of the formation; the total organic carbon (TOC) is computed in accordance with the following relationship: TOC=W _(C_Oil) +W _(C_Bitumen) +W _(C_Kerogen) where W_(C_Oil) is the carbon weight fraction of light oil, W_(C_Bitumen) is a carbon weight fraction of bitumen, and W_(C_Kerogen) is a carbon weight fraction of kerogen; and the reservoir producibility index (RPI) is computed in accordance with the following relationship: RPI=W _(C_Oil) ×W _(C_Oil)/TOC.
 7. A method comprising: using a first downhole tool disposed in a well, obtaining a first well log measurement comprising a multi-dimensional nuclear magnetic resonance measurement using a first downhole tool in the well in a geological formation comprising shale; using the first downhole tool or a second downhole tool disposed in the well, obtaining a second well log measurement that, alone or in combination with the multi-dimensional nuclear magnetic resonance measurement, describes a total organic carbon measurement of the well; and using the first well log measurement and the second well log measurement to compute one or more fluid volumes of hydrocarbon in the well or compute a reservoir producibility index (RPI), or both, and wherein the one or more fluid volumes of hydrocarbon in the well are computed including by: (a) comparing expected T1-T2 nuclear magnetic resonance responses for hydrocarbon to the measured T1-T2 nuclear magnetic resonance responses from the first well log measurement to obtain an estimate of the one or more fluid volumes of the hydrocarbon; (b) computing an uncertainty of the estimate of the fluid volume of the hydrocarbon based at least in part on the second well log measurement; and iteratively performing (a) and (b) using one or more variations of the expected multi-dimensional nuclear magnetic resonance responses for hydrocarbon to cause the uncertainty of the estimate to be reduced or optimized.
 8. The method of claim 7, wherein the reservoir producibility index (RPI) is computed based at least in part on the computed one or more fluid volumes of hydrocarbon in the well. 